Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1096 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1096 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11723484 | C2 | semidirect |
| 3. C3×#63644 | C2 | semidirect |
| 4. C32×#815 | C2 | semidirect |
| 5. #11722036 | C2 | semidirect |
| 11. #88852 | C4 | semidirect |
| 23. #63644 | D3 | semidirect |
| 25. C3×#815 | D3 | semidirect |
| 30. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 34. C33×C8 | C2×C4 | semidirect |
| 74. #815 | C3⋊D3 | semidirect |
| 96. C32×C8 | C4×D3 | semidirect |
| 97. C32×C8 | C4×D3 | semidirect |
| 149. C33 | #442 | semidirect |
| 170. C3×C8 | #624 | semidirect |
| 171. C3×C8 | C4×C3⋊D3 | semidirect |
| 213. C32 | #4711 | semidirect |
| 214. C32 | #4869 | semidirect |
| 223. C8 | #6289 | semidirect |
| 242. C3 | #10590768 | semidirect |
| 243. C3 | #10592410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| #11723484 | 2 |
| C3×#63644 | 2 |
| C32×#815 | 2 |
| #11722036 | 2 |
| #10592410 | 3 |
| #10590768 | 3 |